જો cos(alpha + beta) = frac{4}{5} અને sin(alp | vedclass

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(B) આપેલ છે $\cos(\alpha + \beta) = \frac{4}{5}$. $0 \le \alpha, \beta \le \frac{\pi}{4}$ હોવાથી,$0 \le \alpha + \beta \le \frac{\pi}{2}$,તેથી $	an(\

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$\frac{56}{33}$

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(B) આપેલ છે $\cos(\alpha + \beta) = \frac{4}{5}$. $0 \le \alpha, \beta \le \frac{\pi}{4}$ હોવાથી,$0 \le \alpha + \beta \le \frac{\pi}{2}$,તેથી $	an(\alpha + \beta) = \frac{3}{4}$.આપેલ છે $\sin(\alpha - \beta) = \frac{5}{13}$. તેથી $	an(\alpha - \beta) = \frac{5}{12}$.હવે,$	an 2\alpha = 	an((\alpha + \beta) + (\alpha - \beta))$.$	an 2\alpha = \frac{\frac{3}{4} + \frac{5}{12}}{1 - (\frac{3}{4} 	imes \frac{5}{12})} = \frac{14/12}{33/48} = \frac{56}{33}$.

જો $\cos(\alpha + \beta) = \frac{4}{5}$ અને $\sin(\alpha - \beta) = \frac{5}{13}$,જ્યાં $0 \le \alpha, \beta \le \frac{\pi}{4}$ હોય,તો $\tan 2\alpha = $

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કિંમત શોધો: $\sin (\beta + \gamma - \alpha ) + \sin (\gamma + \alpha - \beta ) + \sin (\alpha + \beta - \gamma ) - \sin (\alpha + \beta + \gamma )$

જો $\cos (\alpha+\beta)=\frac{4}{5}$,$\sin (\alpha-\beta)=\frac{5}{13}$ અને $\alpha, \beta$ એ $0$ અને $\frac{\pi}{4}$ ની વચ્ચે હોય,તો $\tan 2 \alpha$ ની કિંમત શોધો.

સાબિત કરો કે: $(\cos x-\cos y)^{2}+(\sin x-\sin y)^{2}=4 \sin ^{2} \frac{x-y}{2}$

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